# Why do I get inconsistent equations when I resolve forces vertically and perpendicular to the plane? [closed]

Consider a body of mass $m$ kg on a smooth inclined plane inclined at an angle of $\theta$ to the horizontal. Let $R$ be the magnitude of the normal reaction force acting on the body.

If I resolve forces vertically, I get $Rcos\theta=mg$

And if I resolve perpendicular to the plane, I get $R=mgcos\theta$

Clearly this is not possible. What am I doing wrong exactly?

## closed as unclear what you're asking by Bill N, ZeroTheHero, Kyle Kanos, Sebastian Riese, knzhouApr 25 '18 at 10:13

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• What is $R$? A vector magnitude? What is $\theta$? A direction angle? With respect to what? – Bill N Apr 24 '18 at 20:17
• @BillN I’ve edited the question. Hope it’s clearer now. – s.xw Apr 24 '18 at 20:20
• I'm not sure if this is a duplicate, exactly, but it's closely related and might be a duplicate: physics.stackexchange.com/questions/176200/… – David Z Apr 24 '18 at 20:23
• @npojo That should be an answer, not a comment – David Z Apr 24 '18 at 20:24
• Are you using Newton's 1st law on an accelerating object? – Steeven Apr 24 '18 at 20:27

• What if the body is going around a banked corner (circular motion), banked at angle $\theta$ to the horizontal? – s.xw Apr 24 '18 at 20:28
• There is no way around this. If nothing opposes $mgsin\theta$ along the plane, the body will slip down. – npojo Apr 24 '18 at 20:38